Bell Inequalities IntroductionFrom the dawn of the quantum age in 1900, there has been an ongoing debate, often fierce and hostile, between the supporters of the classical world view and those of the quantum world view.This debate eventually led to remarkable experiments, the convincing and repeated results of which are claimed by quantum theorists to support the predictions of quantum mechanics (QM) and not those of classical mechanics (CM).However, old paradigms tend to linger on the shelves of science long past their sell-by dates and there are extant schools of theorists that strive to find loopholes in the above-mentioned experiments.That is a legitimate activity up to a point, but the divisive nature of the debate requires commentary, which is the subject matter of this chapter.QM was discovered only by advanced technology, so it stands to reason that any test of QM will require even more advanced technology.In the previous chapter we stressed the differences between active and passive transformations.The experiments discussed here rely on such technically difficult active transformations that the Hidden Variables (HV) theorists (for that is really what they are) opposing QM are frequently able to think of objections, known as loopholes, to the empirical protocols employed by the experimentalists.Some of these loopholes are reasonable but many are not.Closing those loopholes convincingly is an ongoing important activity in experimental quantum physics.A significant feature of the experiments discussed in this chapter is that they go beyond a certain point of complexity in terms of the number of classical and quantum degrees of freedom involved.Historically, before that point had been reached, classical interpretations of quantum wave functions appeared viable and perhaps even attractive, such as that proposed by Bohm (Bohm, 1952).We shall refer to the collective of such interpretations as the hidden variables (HV) paradigm and the point in question as the Heisenberg point.
Bell Inequalities IntroductionFrom the dawn of the quantum age in 1900, there has been an ongoing debate, often fierce and hostile, between the supporters of the classical world view and those of the quantum world view.This debate eventually led to remarkable experiments, the convincing and repeated results of which are claimed by quantum theorists to support the predictions of quantum mechanics (QM) and not those of classical mechanics (CM).However, old paradigms tend to linger on the shelves of science long past their sell-by dates and there are extant schools of theorists that strive to find loopholes in the above-mentioned experiments.That is a legitimate activity up to a point, but the divisive nature of the debate requires commentary, which is the subject matter of this chapter.QM was discovered only by advanced technology, so it stands to reason that any test of QM will require even more advanced technology.In the previous chapter we stressed the differences between active and passive transformations.The experiments discussed here rely on such technically difficult active transformations that the Hidden Variables (HV) theorists (for that is really what they are) opposing QM are frequently able to think of objections, known as loopholes, to the empirical protocols employed by the experimentalists.Some of these loopholes are reasonable but many are not.Closing those loopholes convincingly is an ongoing important activity in experimental quantum physics.A significant feature of the experiments discussed in this chapter is that they go beyond a certain point of complexity in terms of the number of classical and quantum degrees of freedom involved.Historically, before that point had been reached, classical interpretations of quantum wave functions appeared viable and perhaps even attractive, such as that proposed by Bohm (Bohm, 1952).We shall refer to the collective of such interpretations as the hidden variables (HV) paradigm and the point in question as the Heisenberg point.
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.
Prologue A memorial conference for John Bell, open to the public, was held at Rutgers University around 20 years ago. I gave a short talk there on Bell's views about David Bohm's “hidden variables” formulation of quantum mechanics, a version of quantum mechanics often called the de Broglie–Bohm theory or Bohmian mechanics. This theory was in fact discovered by Louis de Broglie in 1927. In 1952, it was rediscovered and developed by Bohm, who was the first to appreciate its connection to the predictions of standard quantum mechanics. I did not publish the talk. I have decided that it would be appropriate to publish a very lightly edited version of it here, in this volume devoted to the work of Bell on the foundation of quantum mechanics. One reason for doing so is that the connection between Bell and Bohm continues to be somewhat underplayed, with the strength of his advocacy of Bohmian mechanics not properly appreciated. For example, about half of the papers in Bell's collected works on the foundations of quantum mechanics deal with Bohmian mechanics. But in his fine introduction to the revised edition of this great book [1], Alain Aspect mentions this theory in only a single sentence, and parenthetically at that. For several decades after Bell proved his nonlocality theorem, based in part on Bell's inequality, it was widely claimed that Bell had shown that hidden variables – and Bohmian mechanics in particular – were impossible, that they were incompatible with the predictions of quantum mechanics. For example, the great physicist Eugene Wigner, who, unlike most of his contemporaries, was profoundly concerned with the conceptual foundations of quantum mechanics and usually wrote on the subject with great clarity and insight, has written that This [hidden variables] is an interesting idea and even though few of us were ready to accept it, it must be admitted that the truly telling argument against it was produced as late as 1965, by J. S. Bell … This appears to give a convincing argument against the hidden variables theory.
Bell's inequalities(1964) provides a quantitative criterion to test the local hidden variable theory(LHVT) versus quantum mechanics(QM).For the first time,it leads to the possibility to experimentally distinguish LHVT and QM.So far,there have been tens of experiments ever since the first experiment by Clauser et al(1972).An overwhelming majority of these experiments are in good agreement with the predictions of QM yet violate those of LHVT.Some loopholes in these experiments are discussed in Section I,followed by a respective summary to 12 experiments between 1972 to 1982 and 31 experiments from 1985 and on in Sections II and III.It is finally pointed out that so far there is not a single experiment to close both the locality loophole and the detection loophole at the same time,but the experimental outcomes are irreversible.Accordingly,theoretical physicists must admit that the present physics foundation is broken,i.e.quantum mechanics is contradiction with special relativity.
Bell’s inequality is derived by resorting to a hidden-variable theory devised for resolving the Einstein-Bohr debate on the conceptual foundations of quantum mechanics. The legitimacy of quantum superposition for describing the physical world is the essence of the debate. Einstein argued against the legitimacy of quantum superposition. Testing Bell’s inequality by experiment with the experimental result explained by Bell’s theorem opened the door to so-called quantum information technologies. In quantum information theory, “quantum bit” (or “qubit” for short) in a form of quantum superposition is supposed to carry quantum information. Although most physicists believe that Einstein’s vision of the physical world contradicts the experimental result of testing Bell’s inequality, actually neither the experimental result nor Bell’s theorem is relevant to Einstein’s viewpoint. In the present paper, a new principle, the general principle of measurements, is proved as a mathematical theorem. Based on this principle, the experiment for testing Bell’s inequality and so-called experimental evidence for physically realizable “qubit” are scrutinized. The findings are as follows. The experimental result of testing Bell’s inequality and the measurement outcomes of experiments involving “qubit” are all erroneously explained. Bell’s inequality failed to capture the essence of the Einstein-Bohr debate, and Bell’s theorem is irrelevant to Einstein’s vision of the physical world. Quantum mechanics can be completed by using disjunction (“or”) as the logical relation between the orthonormal vectors that span an arbitrarily given Hilbert space without resorting to any hidden-variable theory, while the mathematical setting will remain essentially unchanged. All kinds of “qubit” violate the general principle of measurements and can only describe imaginary objects that do not exist in the physical world. The findings inevitably lead to a very regrettable conclusion: Quantum information has no physical carers and all quantum information technologies are not physically realizable.
Bell’s inequality is derived by resorting to a hidden-variable theory devised for resolving the Einstein-Bohr debate on the conceptual foundations of quantum mechanics. The legitimacy of quantum superposition for describing the physical world is the essence of the debate. Einstein argued against the legitimacy of quantum superposition. Testing Bell’s inequality by experiments with the experimental result explained by Bell’s theorem opened the door to so-called quantum information technologies. In quantum information theory, “quantum bit” (or “qubit” for short) in a form of quantum superposition is supposed to carry quantum information. In the present paper, a new principle, the general principle of measurements, has been proved as a mathematical theorem. Based on this principle, the experiment for testing Bell’s inequality and so-called experimental evidence for physically realizable “qubit” have been scrutinized. The findings are as follows. Although most physicists believe that Einstein’s vision of the physical world contradicts the experimental result of testing Bell’s inequality, neither the experimental result nor Bell’s theorem is relevant to Einstein’s viewpoint, because Bell’s inequality failed to capture the essence of the Einstein-Bohr debate. The experimental result and the measurement outcomes of various experiments involving “qubit” are all erroneously explained. Quantum mechanics can be completed by using disjunction (“or”) as the logical relation between the orthonormal vectors that span an arbitrarily given Hilbert space without resorting to any hidden-variable theory, while the mathematical setting will remain essentially unchanged. All kinds of “qubit” violate the general principle of measurements and can only describe imaginary objects that do not exist in the real world. A very regrettable conclusion from the above findings is inevitable: All quantum information technologies are not physically realizable, because quantum information has no physical carriers.
Bell’s inequality is derived by resorting to a hidden-variable theory devised for resolving the Einstein-Bohr debate on the conceptual foundations of quantum mechanics. The legitimacy of quantum superposition for describing the physical world is the essence of the debate. Einstein argued against the legitimacy of quantum superposition. Testing Bell’s inequality by experiments with the experimental results explained by Bell’s theorem opened the door to so-called quantum information technologies. In quantum information theory, “quantum bit” (or “qubit” for short) in a form of quantum superposition is supposed to represent quantum information. In the present paper, a new principle, the general principle of measurements, is introduced and proved as a mathematical theorem. Based on this principle, the experiments for testing Bell’s inequality and so-called experimental evidence for physically realizable “qubit” are scrutinized. The findings are as follows. Although most physicists believe that Einstein’s vision of the physical world contradicts the experimental results of testing Bell’s inequality, actually Einstein’s viewpoint is irrelevant to Bell’s theorem. Bell’s inequality failed to capture the essence of the Einstein-Bohr debate. The experimental results of testing Bell’s inequality and the measurement outcomes of various experiments involving “qubit” are all erroneously explained. Without involving hidden variables, quantum mechanics can be completed based on the general principle of measurements by using disjunction (“or”) as the logical relation between the orthonormal vectors that span an arbitrarily given Hilbert space, and the mathematical setting can remain essentially unchanged. All kinds of “qubit” violate the general principle of measurements and can only describe imaginary objects that do not exist in the real world. A very regrettable conclusion from the above findings is inevitable: Quantum information has no physical carriers, and all quantum information technologies are not physically realizable.